Nuclear A-dependence near the Saturation Boundary

TL;DR

The paper investigates how the saturation momentum $Q_s$ depends on nuclear size $A$ across three dynamical frameworks: the McLerran-Venugopalan (MV) semiclassical model, fixed-coupling BFKL dynamics, and running-coupling BFKL dynamics. It demonstrates that near the saturation boundary there is robust scaling in all regimes, with $Q_s^2 \\propto A^{1/3}$ in both MV and fixed-coupling cases, while running coupling dynamics lead to an almost complete loss of $A$-dependence in $Q_s^2$ at high energy. The analysis recasts BFKL evolution by treating it in the dipole’s wavefunction, and derives modified saturation scales such as $ar{Q}_s^2(A)$ in the fixed-coupling case to capture logarithmic corrections. These results have implications for interpreting particle production and scaling in heavy-ion collisions across RHIC and LHC energies, suggesting a possible universal saturation behavior in the high-energy, running-coupling regime. Overall, the work clarifies how nuclear size influences saturation dynamics in different QCD evolution pictures and highlights regimes where scaling or universality may emerge.

Abstract

The A-dependence of the saturation momentum and the scaling behavior of the scattering of a small dipole on a nuclear target are studied in the McLerran-Venugopalan model, in fixed coupling BFKL dynamics and in running coupling BFKL dynamics. In each case, we find scaling not too far from the saturation boundary, although for fixed coupling evolution the scaling function for large A is not the same as for an elementary dipole. We find that $Q_s^2$ is proportional to $A^{1/3}$ in the McLerran-Venugopalan model and in fixed coupling evolution, however, we find an almost total lack of A-dependence in $Q_s^2$ in the case of running coupling evolution.